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Fast Fourier transform algorithm computes discrete Fourier transform exactly and is used to considerably speed up the calculations.\\ Note that FFT is not an approximate method of calculation. | Fast Fourier transform algorithm computes discrete Fourier transform exactly and is used to considerably speed up the calculations.\\ Note that FFT is not an approximate method of calculation. | ||

- | MagicPlot uses the algorithm of FFT that does not necessarily require the number of points //N// to be an integer power of 2, though in case of power of 2 evaluation time of the FFT algorithm is less. MagicPlot uses [[http://www.netlib.org/|jfftpack]] library (a Java version of fftpack). | + | {{:fft.png?nolink|}} |

- | | {{:fft1.png|FFT of table columns dialog}} | {{:fft2.png|FFT of curves dialog}} | | + | ===== Parameters ===== |

+ | | ||

+ | ^ Sampling Interval | Sampling interval of original data Δ//t// is used to compute the data in resulting sampling column. MagicPlot calculates sampling interval as a difference between second and first values in ''| | ||

+ | ^ Real, \\ Imaginary of data. \\ If your data is purely real, select ''< | ||

+ | ^ Forward / \\ Inverse | ||

+ | ^ 1/N in forward transform table). If your original data is real, you may want to additionally multiply the result by 2 to get the true amplitudes of real signal. Also referred as ''| | ||

+ | ^ Center zero frequency . | | ||

+ | | ||

+ | ===== Algorithm ===== | ||

+ | | ||

+ | MagicPlot uses the algorithm of FFT that does not necessarily require the number of points //N// to be an integer power of 2, though in such a case evaluation is faster. MagicPlot uses [[http://|jfftpack]] library (a Java version of fftpack). | ||

- | ===== Formulas ===== | ||

==== Discrete Fourier Transform Formulas ==== | ==== Discrete Fourier Transform Formulas ==== | ||

- | By default MagicPlot uses 'Forwart transform is computed using factor '', that the sign of exponential phase factor in Numerical Receipts in C, 2nd edition, p. 503 in forward transform is '' | + | By default MagicPlot uses 'forward transform is computed using factor ''and in MATLAB package in forward transform is '' |

- | ^ ^ Factor −1 (Default) ^ ^ Factor +1 (Scientific) ^^ | + | ^ Factor −1 (Default) |

- | ^ 1/N in forward \\ transform ^ Forward Transform \\ (Signal->^ Forward Transform \\ (Signal-> | + | ^ 1/N in forward \\ transform |

- | ^ Checked \\ (Default) 2 pi i k n {/} N}}</2 pi i k n {/} N}}</ | + | ^ Checked \\ (Default) |

- | ^ Unchecked 2 pi i k n {/} N}}</2 pi i k n {/} N}}</ | + | ^ Unchecked |

- | Here // | + | \\ |

- | The only difference is in the sign of exponential phase factor and 1///multiplier. | + | ^ Factor +1 (Scientific) |

+ | ^ 1/N in forward \\ transform | ||

+ | ^ Checked \\ (Default) 1/N sum{k=1}{N}{c_k e^{2 pi i k n {/} N}}</m> | <N}{C_k e^{−2 pi i k n {/} N}}</ | ||

+ | ^ Unchecked /m> | | ||

- | Note: If you expect to get the original data when doing a inverse FFT of forward FFT set the ''Normalize Forward Transform'' and ''check boxes identically for forward and inverse transforms. | + | |

+ | Here // | ||

+ | | ||

+ | Note: if you expect to get the original data when doing an inverse FFT of forward FFT, set the ''1/N in Forward Transform'', ''and ''for forward and inverse transforms. | ||

==== Amplitude and Phase Columns Formulas ==== | ==== Amplitude and Phase Columns Formulas ==== | ||

- | <m>Amplitude_n = sqrt{{Re_n}^2 + {Im_n}^2},Phase_n = atan2(Im_n, | + | <m>A_n = sqrt{{Re_n}^2 + {Im_n}^2},phi_n = atan2(Im_n, |

- | Because of using [[wp> | + | Because of using ''[[wp>'' function the phase is unwrapped and is in range (//. The result of ''. |

==== Sampling Column Formulas ==== | ==== Sampling Column Formulas ==== | ||

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* Missing values in the end of the column are ignored. | * Missing values in the end of the column are ignored. | ||

- | ===== Parameters ===== | + | ===== See Also ===== |

- | ^ Sampling Interval | + | * [[processing]] |

- | ^ Real, \\ Imaginary | + | |

- | ^ Forward / \\ Inverse | + | |

- | ^ 1/N in forward transform | + | |

- | ^ Center zero frequency | | + |

fft.1288073133.txt.gz · Last modified: Sun Nov 8 12:20:32 2015 (external edit)

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